Introduc)on to Neutrino Physics

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ν _e ν _µ ν _τ

Introduc)on to Neutrino Physics

Lecture 1

Neutrino oscilla0ons Part I

Elisabeth Falk

University of Sussex and Lund University

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Neutrino

• “The liAle neutral one” in Italian

• A subatomic par0cle with almost no mass, no charge, no magne0c moment, and which interacts only rarely

• Neutrinos make up the same frac0on of mass in the universe as stars and planets do

• They exhibit bizarre behavior when travelling through space: They change form from one type of neutrino to another. No other par0cle does this

28/11/11 E. Falk, U. of Sussex and Lund U. 2

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Overview of lecture course

• Introduc0on to the

course and to neutrinos

• Neutrino oscilla0on formalism

• “Solar” neutrinos

• Atmospheric and long-‐

baseline neutrinos

• θ ₁₃ and CP viola0on

• Neutrino mass,

Majorana neutrinos, the see-‐saw

mechanism

• Neutrinoless double beta decay: theory and experiment

• “The neutrino speed of light thing” –

OPERA

• SN1987a (hopefully!)

• Wrap-‐up and outlook

~ L1

&

L2+

~ L3-‐

&

L4

~

L5

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Outline lecture 1

• Neutrinos: introduc0on and a liAle history

• Neutrino oscilla0on formalism:

two-‐ and three-‐neutrino oscilla0ons

• Solar neutrinos (con0nued tomorrow)

• Suggested reading

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The discovery of the neutrino

• 1920s: Puzzle: Radioac0ve β decay appears to

break energy conserva0on: electron has con0nuous spectrum!

• 1930: “Desperate remedy”: Wolfgang Pauli suggests new par0cle carrying oﬀ missing energy without being detected

• 1933: Enrico Fermi formulates comprehensive theory of radioac0ve decays

– Pauli’s par0cle crucial

– “Neutrino” – the liAle neutral one

• 1956: Fred Reines and Clyde Cowan detect neutrinos created by nuclear reactor

– Savannah River, South Carolina, USA – Case of champagne from Pauli

– 1995 Nobel Prize (Reines)

W. Pauli

E. Fermi

C. Cowan and F. Reines

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The discovery of the neutrino

• 1962: Leon Lederman, Mel Schwartz and Jack Steinberger detect muon neutrinos

– Created neutrino beam at accelerator lab (Brookhaven, NY) – 1988 Nobel Prize

• 2000: DONUT collabora0on sees ﬁrst direct evidence of tau neutrino

– Fermilab, Chicago

C. Cowan and F. Reines

L. Lederman, M. Schwartz and J. Steinberger

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Lots of neutrinos!

Supernova explosions

Cosmic rays hikng the atmosphere produce neutrinos

Relics from the Big Bang:

30 million neutrinos in each of us!

Together with microwave radia0on make up cosmic background radia0on

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Lots of neutrinos!

• Nuclear fusion:

– Mainly from pp cycle:

4 p combine with 2 e ^-‐ to form a He ²⁺ and 2ν _e

• 100 billion neutrinos from the sun pass through each of your ﬁngernails—every second!

But most of the neutrinos passing through us

come from the sun

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Elusive neutrinos

"The chances of a neutrino actually hitting something as it travels through all this

howling emptiness [that is the Earth] are

roughly comparable to that of dropping a ball bearing at random from a cruising 747 and

hitting, say, an egg sandwich."

-- Douglas Adams, (1952-2001)

This happens to be correct: see

hAp://faculty.oAerbein.edu/NTagg/OAerbein/Publica0ons_ﬁles/eggsandwich.pdf

for the calcula0on

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Why do we care?

• Fundamental part of nature

• Poorly understood, compared to other nature’s other building blocks

For example:

• What are the neutrino masses?

• What is the paAern for neutrino ﬂavour mixing?

• Is the neutrino its own an0par0cle?

– The ul0mate neutral par0cle

• Do neutrinos violate CP?

• Do neutrinos cons0tute dark maAer?

• What can neutrinos and the universe tell us about each other?

• Can neutrinos help explain the maAer-‐an0maAer asymmetry in the universe?

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Massive neutrinos

Neutrino mass eigenstates are not the same as the ﬂavour eigenstates u

d

µ

⁺

ν

_µ

W

⁺

ν

₁

ν

₃

ν

₂

Flavour eigenstate

produced in

weak interac0on

Superposi0on of

mass eigenstates

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Current situa0on

ν _µ

ν _τ ν _e

ν ₁ ν ₂ ν ₃

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Neutrino oscilla0ons: concept

• Write down the rela0on between mass eigenstates and ﬂavour eigenstates as a rota0on with angle θ:

• The mass eigenstates have diﬀerent momenta and thus travel at slightly diﬀerent speeds: get out of phase

– IF masses are diﬀerent!

– Assump0on: energy is the same

• Detec0on probability for a given ﬂavour changes with distance travelled

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Neutrino oscilla0ons: concept

Two ﬂavours:

Three ﬂavours:

θ

3-‐D complex rota0on

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Oscilla0on amplitude

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Outline of deriva0on

1. Weak eigenstates ν

_α

in terms of mass eigenstates ν

_k

:

2. Transi0on probability ν

_α

 ν

_β

from amplitude squared:

3. For ultrarela0vis0c neutrinos (E >> m):

where energy eigenvalues:

where and

4. Using distance travelled L instead of 0me t (t = L, as neutrino speed ≈ c):

Neglec0ng mass

contribu0on

Assuming plane wave

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Two-‐neutrino oscilla0ons

Using

with result from previous slide,

transi0on probability becomes:

Physical constants

Experimental

parameters

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Two-‐neutrino oscilla0ons

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Three-‐neutrino oscilla0ons

€

U

_PMNS

=

1 0 0

0 cosθ

₂₃

sinθ

₂₃

0 −sinθ

₂₃

cosθ

₂₃

⎛

⎝

⎜

⎜ ⎜

⎞

⎠

⎟

⎟ ⎟ ×

cosθ

₁₃

0 e

⁻ⁱ^δ^CP

sinθ

₁₃

0 1 0

−e

⁻ⁱ^δ^CP

sinθ

₁₃

0 cosθ

₁₃

⎛

⎝

⎜

⎜ ⎜

⎞

⎠

⎟

⎟ ⎟

×

cosθ

₁₂

sinθ

₁₂

0 −sinθ

₁₂

cosθ

₁₂

0 0 0 1

⎛

⎝

⎜

⎜ ⎜

⎞

⎠

⎟

⎟ ⎟ × U

_Maj^diag

Mixing matrix U

_PMNS

can be factored into three 2-‐D rota0onal matrices × U

_maj

(diagonal, so not relevant for oscilla0ons)

Three independent mixing angles

CP-‐viola0on phase

€

U

_PMNS

Pontecorvo-Maki-

Nakagawa-Sakata

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Mass hierarchy

We don’t know the ordering the mass splikngs Δm

₂

– but we do know that ν

₂

>> ν

₁

ν

₃

Δm

²₃₂

"

Δm

²₂₁

"

ν

₂

ν

₁

ν

_e

ν

_τ

ν

_µ

(mass)

²

ν

₃

Δm

²₂₁

"

ν

₂

ν

₁

Δm

²₃₂

"

Normal hierarchy Inverted hierarchy

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Current knowledge

28/11/11 21

€

U

_PMNS

=

1 0 0

0 cosθ

₂₃

sinθ

₂₃

0 −sinθ

₂₃

cosθ

₂₃

⎛

⎝

⎜

⎜ ⎜

⎞

⎠

⎟

⎟ ⎟ ×

cosθ

₁₃

0 e

⁻ⁱ^δ^CP

sinθ

₁₃

0 1 0

−e

⁻ⁱ^δ^CP

sinθ

₁₃

0 cosθ

₁₃

⎛

⎝

⎜

⎜ ⎜

⎞

⎠

⎟

⎟ ⎟

×

cosθ

₁₂

sinθ

₁₂

0 −sinθ

₁₂

cosθ

₁₂

0 0 0 1

⎛

⎝

⎜

⎜ ⎜

⎞

⎠

⎟

⎟ ⎟ × U

_Maj^diag

CP-‐viola0on

phase

θ

₁₃

<~ 10

^o

Δm

²₃₁

~ Δm

²₃₂

~Unknown

€

cosθ

₁₃

0 e

⁻ⁱ^δ^CP

sinθ

₁₃

0 1 0

−e

⁻ⁱ^δ^CP

sinθ

₁₃

0 cosθ

₁₃

⎛

⎝

⎜

⎜ ⎜

⎞

⎠

⎟

⎟ ⎟

Well measured:

θ

₂₃

= (45 ± 7)

^o

-‐> ~equal mixing of ν

_µ

and ν

_τ

Δm

²₃₂

≈

Δm

²_atm

= 2.4

^x

10

^-‐3

eV

²

“Atmospheric” from atmosphere and

accelerators

Un0l this summer ~unknown:

θ

₁₃

<~ 10

^o

Now ~3σ indica0ons that θ

₁₃

< 10

^o

|Δm

²₃₁^|

≈ Δm

²₃₂

but Δm

²₃₁

> 0 or < 0

(normal or inverted hierarchy)?

“Subdominant”

or “third” CP-‐viola0on phase = ?

Well measured:

θ

₁₂

= (34 ± 3)

^o

-‐> ν

₁

is predominantly ν

_e

Δm

²₂₁

= 7.6

^x

10

^-‐5

eV ν

₂

> ν

₁

(sign of Δm

²₂₁

) from maAer eﬀects in sun

“Solar” from sun + reactors

E. Falk, U. of Sussex and Lund U.

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MaAer oscilla0ons

1. Low electron density (the Earth):

2. Resonant MSW:

θ _M = π/4

Total transi0on

between two ﬂavours 3. Varying N _e (the Sun):

dθ _M /dx ≠ 0

Adiaba0c transi0on

between eﬀec0ve mass eigenstates

Linc Wolfenstein (1978)

MSW eﬀect:

Electron neutrinos feel a “drag”

due to extra contribu0on from W exchange

Eﬀec)ve θ _M and Δm ²

N

_e

= electron density

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Energy produc0on in the sun

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Neutrino produc0on in the sun

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E. Falk, U. of Sussex and Lund U.

40 years ago:

Homestake chlorine experiment

 First experiment to study neutrinos from the sun

 Homestake Gold Mine, South Dakota, USA

 Big tank of chlorine-‐based cleaning ﬂuid

 ν

_e

+

³⁷

Cl 

³⁷

Ar + e

^-‐

 Counted electron neutrinos (ν

_e

)

 Saw 1/3 of neutrinos expected from luminosity

 The “solar neutrino problem”

 Ray Davis: Nobel Prize 2002

R. Davis

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Experimental techniques

e

µ ^-

Elas0c scaAering of neutrinos on electrons Charged lepton produces Cherenkov radia0on CC contribu0on 6.8 x NC contribu0on

 much enhanced for ν

_e

Gallium experiments

Water Cherenkov experiments

Liquid-‐scin)llator detectors

Neutrinos: Elas0c scaAering on electrons An0-‐neutrinos (reactor):

Inverse beta decay: ν

_e

+ p → n + e

⁺

Diﬀerent

ν energy

thresholds

with diﬀerent

techniques

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The solar neutrino problem

Solved in 2002 by SNO

More in Lecture 2

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Recap and outlook

• The neutrino is the least understood of our fundamental par0cles, but may hold the answer to many exci0ng

ques0ons about the universe as well as par0cle physics

• Neutrinos oscillate between diﬀerent ﬂavours because they have non-‐zero mass AND their mass eigenstates are

diﬀerent from their ﬂavour eigenstates

• The study of neutrinos from the sun showed an apparent deﬁcit of neutrinos – we know now that it is due to

oscilla0ons

• More on neutrino oscilla0ons tomorrow!

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• C. Giun0 and C. W. Kim,

Fundamentals of Neutrino Physics and Astrophysics, Oxford University Press 2007

• F. Close, Neutrino, Oxford University Press 2010

• Deriva0on of neutrino oscilla0ons:

PhD theses, .e.g., B. S0ll, T2K ND280 π

₀

Electromagne0c Calorimeter, University of Sheﬃeld 2009

– Ben also runs a neutrino blog: hAp://

neutrinoscience.blogspot.com/

• Par0cle Data Group review: hAp://

pdg.lbl.gov/2010/reviews/rpp2010-‐

rev-‐neutrino-‐mixing.pdf

• H. Lipkin, Neutrino oscilla0ons as two-‐slit experiments in momentum space, Phys. LeA. B477 (2000)

195-‐2000

• B. Kayser, On the quantum mechanics of neutrino oscilla0on, Phys. Rev. D24 (1981) 110-‐116

• B. Kayser, Neutrino Oscilla0on

Phenomenology , hAp://arxiv.org/pdf/

0804.1121

• Neutrino Oscilla0on Industry: /hAp://

www.hep.anl.gov/ndk/hypertext

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Introduc)on to Neutrino Physics

ν e ν µ ν τ